Seminar| Institute of Mathematical Sciences
Time: Friday, October 30th, 2026,16:00-17:00
Location: IMS S408
Speaker: Zhou Yang (杨舟), South China Normal University
Abstract:This paper investigates the finite-horizon optimal investment-consumption problem with voluntary retirement and upper and lower bounds on consumption, which can be formulated as a mixed stochastic control problem coupling stopping and constrained regular controls. Different from the conventional duality method for such problems, we adopt a direct approach in this paper: we first derive the Hamilton-Jacobi-Bellman equation for the original mixed control problem, and obtain its dual equation via the Legendre transformation; then, we analyze the analytical properties of the solution and free boundaries to the dual equation based on partial differential equation theory; finally, we prove the corresponding verification theorem using these properties, and theoretically study the key characteristics of the optimal strategies, focusing on the regularity of the three free boundaries (the optimal retirement boundary, the upper consumption boundary and the lower consumption boundary) as well as their monotonicity with respect to the initial time, initial wealth and model parameters.